Hydrogen may interact with hydrogen-storage materials (HSM) by means of chemi- or physisorption. In the case of chemisorption, molecular hydrogen (dihydrogen) is dissociated and adsorbed as atomic hydrogen with relatively large binding energies. Physisorbed hydrogen is characterized by very weak interactions between intact dihydrogen and the HSM. This talk focuses on physisorption, that is, on the quantum chemical calculation of the van der Waals interactions between dihydrogen and various other molecules or materials. The accurate and reliable calculation of such weak interactions poses a challenge for modern quantum chemistry for several reasons: (1) Dispersion forces are not captured by density-functional theory; (2) Electron-correlation methods suffer from high scaling of computational effort as well as from very slow basis-set convergence; (3) Supramolecular calculations of small interaction energies are easily corrupted by basis-set superposition errors. This talk will address these issues and present examples of how accurate and reliable quantum chemical calculations can be conducted in spite of the difficulties.